This application relates to representing computer models and more particularly to representing a geometry model at more than one level of resolution.
The accurate representation of subsurface topology can have a profound effect on the interpretation of a geoscience model. This is mainly due to the presence of material properties such as, for example, oil. For a more detailed introduction on the importance of topology, see U.S. patent application Ser. No. 08/772,082, entitled MODELING GEOLOGICAL STRUCTURES AND PROPERTIES.
Imagine, for example, the situation of two compartments 10a, 10b separated by a sealed fault 12 (a sealed fault is an impermeable membrane that does not permit fluids to pass), as shown in FIG. 1. Due to the sealed fault there can be no flow of fluid from compartment 10a to compartment 10b. If both compartments were to contain oil it would be necessary to drill into both compartments to recover the oil.
Now suppose the sealed fault 12 is punctured, as shown in FIG. 2. There is now a free flow of fluid between compartment 10a and compartment 10b so it would be possible to drill just into one of the compartments to extract the oil.
Thus, having the correct topology in the geoscience model can have a profound effect on the finances of an oil-field development.
Another important concept in interpreting geoscience models presented graphically on a computer screen is the concept of multiresolution analysis, whereby an analyst can view an area of interest in the geoscience model at different resolution levels. There are many techniques that have been developed for multiresolution analysis of surfaces. The work falls into two principal categories. The first is to use wavelets. The second is to use edge contraction and edge flipping, which is sometimes called "topological editing".
Wavelets have found wide acceptance in image processing and recently have found application in surface representations. Typically, wavelets are used in a subdivision fashion. A typical subdivision scheme uses quaternary subdivision. For example, as shown in FIG. 3, a triangle 14 may be subdivided into four triangles 16a-d. In the example shown in FIG. 3, the retessellation conforms to the subdivision scheme. That is, the retessellation of the triangle into four triangles conforms with the quaternary subdivision scheme. It can be imagined, however, that if a different local retessellation of the triangle is performed, it may not be clear how to rebuild the subdivision scheme, since the refinement may not conform to the subdivision scheme. For example, if the triangle 14 is retessellated as in FIG. 3b into triangles 17a and 17b, the retessellation does not conform to the quaternary subdivision scheme. There has been no work on the integration of wavelets and boundary representations.
Topological editing, or editing a mesh using the topological operations of vertex removal, edge contraction and edge flipping, can be used to build multiresolution surfaces. Some mesh building techniques build a history of topological operations which permits progressive and partial loading of the surface, but it is not clear how this history is modified if a triangle is refined. There has been no work on the integration of topological editing and boundary representations.